EXOSAT results obtained with the imaging instrument (CMA) and the medium energy proportional counters (ME) are discussed. Assuming that the featureless power-law spectrum obtained in the 2 to 10 keV range is synchrotron radiation from relativistic electrons, one derives constraints on magnetic field strength and age of the nebula. The energy spectra of the electrons responsible for the emission in the radio and X-ray ranges are discussed. The great similarity of the physical properties of G 29.7-0.3 and of three synchrotron nebulae containing a compact object observed to pulse in X-rays makes G 29.7 - 0.3 a very promising candidate for further search for pulsed emission. Further observations at infrared wavelengths might reveal the break(s) in the emitted spectrum expected from the radio and X-ray power-law indices and give us more information on the production of the electron populations responsible for the emission of the nebula.